Refinement of a Hardy–Littlewood–Pólya-type inequality for powers of self-adjoint operators in a Hilbert space

The well-known Taikov’s refined versions of the Hardy – Littlewood – Pólya inequality for the $L_2$-norms of intermediate derivatives of a function defined on the real axis are generalized to the case of powers of self-adjoint operators in a Hilbert space.